The impact of financial development on economic growth has received much attention in the recent literature. The general conclusion is that development of the financial sector is positively related to the level of growth. However, theoretical studies have espoused discontinuities in the relationship. More importantly, the relationship between finance and economic activity is well mediated by the level of initial per capita income, human capital and existing financial development. While this is well documented at the theoretical front, empirical literature is silent on the nonlinearities in finance–growth nexus caused by the threshold variables. Beyond examining the impact of financial development on economic growth for 29 SSA countries over the period 1980–2014, in this study, we further investigate whether the impact of finance on growth is conditioned on the initial levels of countries’ income, human capital and financial sector development. Our overall finding is that, financial development is positively and significantly associated with economic growth. However, the growth–enhancing effect of finance is higher when measured with private relative to domestic credit. We re–examine the threshold effect of finance in the face of the threshold variables. Our evidence suggests that, in almost all cases, financial sector development is positively related to growth albeit insignificantly below the estimated thresholds. The only exception is the impact of private credit on growth below the income threshold where the impact is slightly significant. Similar trend is also noticed when domestic credit mediates the finance–growth nexus.